## Dividend Discount Models

When an investor buys stock, he generally expects to get two types of cash flows -dividends during the holding period and an expected price at the end of the holding period. Since this expected price is itself determined by future dividends, the value of a stock is the present value of just expected dividends. The dividend discount model is therefore the most direct and the most conservative way of valuing a stock since it counts only those cashflows that are actually paid out.

### Setting up the Model

In it's most general form, the value of a stock in the dividend discount model is the present value of the expected dividends on the stock in perpetuity.

Expected Dividends in period t

Value per share of stock = #

Terminal Value: This is the expected price of a stock (or equity) at the end of a specified holding period.

t=1 (1+ Cost of Equity)1 Since we cannot estimate dividends in perpetuity, we generally allow for a period where dividends can grow at extraordinary rates but we allow for closure in the model by assuming that the growth rate will decline to a stable rate that can be sustained forever at some point in time in the future. By assuming stable growth at some point in time in the future, we can stop estimating dividends and estimate what we think the stock will be worth at the end of the extraordinary growth period.

Terminal Value

Value0 =

E(Dividends)t Terminal Valuen , ^ , TT , E(Dividends)n+1

where r is the cost of equity and gn is the expected growth rate in dividends in perpetuity after year n.2 Note that it is possible for a firm to already be in stable growth, in which case this model collapses into itls simplest form:

Value of a stock in stable growth = Expected Dividends next year/ (Cost of equity - gj This model is called the Gordon Growth model and is a special case of the dividend discount model. It can be used only for firms that are already in stable growth.3

### Estimating Model Inputs

Breaking down the general version of the dividend discount model, there are four basic components. The first is the length of the high growth period, during which the firm can sustain extraordinary growth. The second is the expected dividends each year during the high growth period. The third is the cost of equity that stockholders will demand for holding the stock, based upon their assessments of risk. The final input is the expected price at the end of the high growth period - the terminal value. In this section, we will consider the challenges associated with estimating each of these components.

a. Length of High-Growth Period

The question of how long a firm will be able to sustain high growth is perhaps the most difficult of all to answer in a valuation, but two points are worth keeping in mind. One is that it is not a question of whether but when; all firms will ultimately be stable growth firms, because high growth makes firms larger, and the firm's size will eventually become a barrier to further high growth. The second is that high growth in valuation, at least high growth that creates value, comes from firms earning high returns on their marginal investments. Using the terminology that we have used before in investment analysis, it comes from firms having a return on equity (capital) that is well in excess of the cost of equity (capital). Thus, when we assume that a

2 The cost of equity can be different for the high growth and stable growth periods. Hence, rn is the cost of equity for the stable growth period.

3 When the Gordon Growth model is used to value high growth companies, it is entirely possible that g>r and the model will yield a negative value. The problem is not with the model but in its msapplication to a high growth firm.

High Growth Period: This is a period during which a company's earnings or cash flows are expected to grow at a rate much higher than the overall growth rate of the economy.

firm will experience high growth for the next 5 or 10 years, we are also implicitly assuming that it will earn excess returns (over and above the cost of equity or capital) during that period. In a competitive market, these excess returns will eventually draw in new competitors, and the excess returns will disappear.

We should look at three factors when considering how long a firm will be able to maintain high growth.

1. Size of the firm: Smaller firms are much more likely to earn excess returns and maintain these excess returns than otherwise similar larger firms. This is so because they have more room to grow and a larger potential market. When looking at the size of the firm, we should look not only at its current market share, but also at the potential growth in the total market for its products or services. Thus, Microsoft may have a large market share of the computer software market, but it may be able to grow in spite of it because the entire software market is growing. On the other hand, Boeing dominates the market for commercial airliners, but we do not expect the overall market for airliners to increase substantially. Boeing, therefore, is far more constrained in terms of future growth.

2. Existing growth rate and excess returns: Although the returns we would like to estimate are the marginal returns on new investments, there is a high correlation between the returns on current investments and these marginal returns. Thus, a firm earning excess returns of 20% on its current investments is far more likely to have large positive excess returns and a long growth period than a firm currently earning excess returns of 2%. There are cases where this rule will not work, such as in new industries going through major restructuring.

3. Magnitude and Sustainability of Competitive Advantages: This is perhaps the most critical determinant of the length of the high growth period. If there are significant barriers to entry and sustainable competitive advantages, firms can maintain high growth for longer periods. If, on the other hand, there are no or minor barriers to entry, or if the firm's existing competitive advantages are fading, we should be far more conservative about allowing for long growth periods. The quality of existing management also influences growth. Some top managers4 have the capacity to make the strategic choices that increase competitive advantages and create new ones. Again, the sensitivity of value to changes in the length of the high growth period can always be estimated. While some analysts use growth periods greater than 10 years, the combination of high growth rates and long growth periods creates a potent mix in terms of increasing the size of the firm, in many cases well beyond the realm of what is reasonable. Looking back, there are very few firms that have been able to grow at high rates for more than 10 years.

Illustration 12.1: Length of High Growth Period

To assess how long high growth will last at Disney, Aracruz and Deutsche Bank, we assessed their standings on each of the above characteristics in Table 12.1:

## Lessons From The Intelligent Investor

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